r = 12 sin 18ti + 12 cos 18tj

Q: if x ≤ 2 f(x)= [2x - 5], if 2 3 1. Determine if f is continuous or discontinuous at r = 2 and r =…

A: Solution of the problem as follows

Q: Use the figure to derive the formulas for sin sin(). = $(€). [ COS tan TOIN cos e 6 (2). sin 0 cos…

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Q: Find the tangent line approximation to the graph off at the given point. Then complete the table.…

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Q: (D² - D-2)y = cos x

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

A: Let's find.

Q: Radius of Convergence of a Power Series. (n!)x" Determine the radius of convergence for the series…

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Q: Describe the graph of the equation. r = 7costi 14 sin tj + k O An ellipse in the plane x = 1, center…

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = 3 cost-2 sint,…

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Q: Write the Taylor series for f(x) = xº about x = −4 as Σ Cn (x + 4)". n=0 Find the first five…

A: The given function is  f(x)=x3 about x=-4.

Q: More on Areas. Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence…

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Q: chapman corporation

A: answer is in next step

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e, y = 1…

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Q: Evaluate (F JC Er F • dr. F(x, y) = xi + yj C: r(t) = (7t + 4)i + tj, 0≤t≤1

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Q: Write the Taylor series for f(x) = x³ about x = −2 asen(x+2)". n=0 Find the first five coefficients.…

A: Given that      f(x) = x3

Q: Monique sells disposable protective face masks made of local textiles for P 12.00 each. Define a…

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Q: what is the derivate of sin(x)cos(x)?

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Q: Find the volume of the shaded region when revolved about the indicated axis. Y A B D 493 392 334 234…

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Q: Find the volume of the solid obtained by revolving y(x) = sin(7x) for 0 ≤ x ≤ about the x-axis. (Use…

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Q: Applying the ratio test to the series ∞ 5k-1 k=1 (k+ 1)².4k ³ you would compute ak+1 lim = ak Hence…

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Q: 2. y = tan (cosh x) (sin x)(sech x) secx (use logarithmic differentiation)

A: As per the requirement of the student question number 2 has been solved. Here we need to calculate…

Q: Problem 3

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Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: What are the rectangular coordinates of the point whose spherical coordinates are (1, ½π, π) ? x = Y…

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Q: Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying…

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs x = y³ and x = y…

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Q: Find the first four nonzero terms of the Taylor series about 0 for the function f(x) = √1+x cos(3x).…

A: We need to find polynomial series.

Q: Solve the following differential equations of d² y dx² dx dy +3 dv −10y=3x²

A: We have to find the solution of the given differential equation.

Q: Find the derivative of the function. f(t) = (9t+ 9)2/3 f"(t): =

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Q: What are the cylindrical coordinates of the point whose spherical coordinates are (3, 5, 1)? r = 0 =…

A: Given: spherical coordinates ρ,θ,φ, here ρ=3,θ=5φ=π6 To find : cylindrical coordinates r, θ, z

Q: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +7 1 lim t +∞o (?, ?) 5t² + 6'5t,

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Q: (a) Write a sum formula for sin(u + v + w). sin(u + v + w) = (b) Write a sum formula for tan(u + v +…

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Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: Find a power series representation for the function. (Give your power series representation centered…

A: We have to find the Power series representation.

Q: the type of conic section whose equation is giv x² - 2x + 2y² - 20y + 49 = 0 rabola ipse perbola…

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Q: Find the average value of the function f(x) = 3x³ on the interval 2 ≤ x ≤ 6

A: The average value of a function is found by taking the integral of the function over the interval…

Q: Evaluate the integral 13 ƒ(x)dx geometrically for ƒ (x) = { |3 − x ; x ≤ 5 2; x > 5

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Q: Find the exact length. T=0², 0≤0 ≤ 2π ° 4[G²+1²] ²3 [(x² + 1)² - 1] [(²+1)-1] ° 4[68² +1²]

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Q: Evaluat the integral. Q₁ is's ex dxdy 3y +²

A: Here we have to find the integral.

Q: Sketch the region enclosed by the curves x = sin 3y and x = y, and compute its area as an integral.…

A: We have to find the area between the curves.

Q: Replace the polar equation with an equivalent Cartesian equation. r= 40 sin 0

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Q: [2,

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Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

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Q: of a rectangle.

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Q: Solve the following differential equations of d²y dy dx² +==X dx

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Q: 15. Sketch y = f(x). Properties are: Max at P(2, 2) Mins at Q(4, -1), R(-1,2). Oblique asymptote y =…

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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Q: Determine two coterminal angles in degree measure (one positive and one negative) for each angle.…

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